What is 19/28 plus 15/21? (Answer: 39/28)

Exact Answer

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Problem: What is 19/28 plus 15/21?
Formula / Expression: 19/28 + 15/21
Final Answer: 1 11/28 (39/28)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).
Working: LCD(28, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 19/28 by 3, and multiply the numerator and denominator of 15/21 by 4 so both fractions share the common base 84.
Working: 19 × 3/28 × 3 = 57/84 and 15 × 4/21 × 4 = 60/84

Step 3: Add the Numerators
Now add the numerators (57 + 60 = 117) and keep the common denominator 84 unchanged.
Working: 57 + 60/84 = 117/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 84, which is 3. Divide both the numerator and denominator by 3.
Working: 117 ÷ 3/84 ÷ 3 = 39/28

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (39) is greater than the denominator (28), divide 39 by 28: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/28.
Working: 39/28 = 1 11/28

Step 6: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 28 produces a repeating decimal (approximately 1.392857, or 139.2857%).
Working: 39 ÷ 28 = 1.392857 (139.2857%)

Key Values:
- Simplified Fraction: 39/28
- Mixed Number Form: 1 11/28
- Decimal Value: 1.392857
- Percentage: 139.2857%

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Solved with FractionsCalc:
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19/28 + 15/21 = 39/28

Simplified Fraction

39/28

Mixed Number

1 11/28

Decimal Value

1.392857

Percentage

139.2857%

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Step-by-Step Solution: 19/28 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 28 × 21 = 588, keeping the calculation simpler).

LCD(28, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 19/28 by 3, and multiply the numerator and denominator of 15/21 by 4 so both fractions share the common base 84.

19 × 3/28 × 3 = 57/84 and 15 × 4/21 × 4 = 60/84

Step 3

Add the Numerators

Now add the numerators (57 + 60 = 117) and keep the common denominator 84 unchanged.

57 + 60/84 = 117/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 117 and 84, which is 3. Divide both the numerator and denominator by 3.

117 ÷ 3/84 ÷ 3 = 39/28

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (39) is greater than the denominator (28), divide 39 by 28: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/28.

39/28 = 111/28

Step 6

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 28 produces a repeating decimal (approximately 1.392857, or 139.2857%).

39 ÷ 28 = 1.392857 (139.2857%)

Visual Representation

The diagram below illustrates 19/28 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/28`
Mixed Number Form	`1 11/28`
Decimal Form	`1.392857`
Percentage	`139.2857%`

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Frequently Asked Questions

What is 19/28 plus 15/21 as a fraction?

19/28 + 15/21 in simplest fraction form is 39/28 (or 1 11/28 as a mixed number).

What is 19/28 plus 15/21 as a decimal?

19/28 + 15/21 converted to a decimal is 1.392857.

What is 19/28 plus 15/21 as a percentage?

19/28 + 15/21 expressed as a percentage is 139.2857%.

How do you write 19/28 plus 15/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 39/28 can be written as the mixed number 1 11/28.

Does 19/28 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.392857...) because the denominator contains prime factors other than 2 and 5.